Showing papers on "Boundary layer published in 1971"

Orderly Structure in Jet Turbulence

Abstract: Past evidence suggests that a large-scale orderly pattern may exist in the noiseproducing region of a jet. Using several methods to visualize the flow of round subsonic jets, we watched the evolution of orderly flow with advancing Reynolds number. As the Reynolds number increases from order 102 to 103, the instability of the jet evolves from a sinusoid to a helix, and finally to a train of axisymmetric waves. At a Reynolds number around 104, the boundary layer of the jet is thin, and two kinds of axisymmetric structure can be discerned: surface ripples on the jet column, thoroughly studied by previous workers, and a more tenuous train of large-scale vortex puffs. The surface ripples scale on the boundary-layer thickness and shorten as the Reynolds number increases toward 105. The structure of the puffs, by contrast, remains much the same: they form at an average Strouhal number of about 0·3 based on frequency, exit speed, and diameter.To isolate the large-scale pattern at Reynolds numbers around 105, we destroyed the surface ripples by tripping the boundary layer inside the nozzle. We imposed a periodic surging of controllable frequency and amplitude at the jet exit, and studied the response downstream by hot-wire anemometry and schlieren photography. The forcing generates a fundamental wave, whose phase velocity accords with the linear theory of temporally growing instabilities. The fundamental grows in amplitude downstream until non-linearity generates a harmonic. The harmonic retards the growth of the fundamental, and the two attain saturation intensities roughly independent of forcing amplitude. The saturation amplitude depends on the Strouhal number of the imposed surging and reaches a maximum at a Strouhal number of 0·30. A root-mean-square sinusoidal surging only 2% of the mean exit speed brings the preferred mode to saturation four diameters downstream from the nozzle, at which point the entrained volume flow has increased 32% over the unforced case. When forced at a Strouhal number of 0·60, the jet seems to act as a compound amplifier, forming a violent 0·30 subharmonic and suffering a large increase of spreading angle. We conclude with the conjecture that the preferred mode having a Strouhal number of 0·30 is in some sense the most dispersive wave on a jet column, the wave least capable of generating a harmonic, and therefore the wave most capable of reaching a large amplitude before saturating.

On the Boundary Condition at the Surface of a Porous Medium

Abstract: A theoretical justification is given for an empirical boundary condition proposed by Beavers and Joseph [1]. The method consists of first using a statistical approach to extend Darcy's law to non homogeneous porous medium. The limiting case of a step function distribution of permeability and porosity is then examined by boundary layer techniques, and shown to give the required boundary condition. In an Appendix, the statistical approach is checked by using it to derive Einstein's law for the viscosity of dilute suspensions.

The production of turbulence near a smooth wall in a turbulent boundary layer

Abstract: The structure of the flat plate incompressible smooth-surface boundary layer in a low-speed water flow is examined using hydrogen-bubble measurements and also hot-wire measurements with dye visualization. Particular emphasis is placed on the details of the process of turbulence production near the wall. In the zone 0 < y+ < 100, the data show that essentially all turbulence production occurs during intermittent ‘bursting’ periods. ‘Bursts’ are described in some detail.The uncertainties in the bubble data are large, but they have the distinct advantage of providing velocity profiles as a function of time and the time sequences of events. These data show that the velocity profiles during bursting periods assume a shape which is qualitatively distinct from the well-known mean profiles. The observations are also used as the basis for a discussion of possible appropriate mathematical models for turbulence production.

Chemically Reacting Viscous Flow Program for Multi-Component Gas Mixtures.

Abstract: A general computer program was developed for solving the laminar boundary layer equations with a finite-difference method. The governing equations are solved in an uncoupled manner in order that a gas mixture with a large number of chemical species can be readily handled. The program has been written with various options to provide a flexibility that allows a variety of problems to be solved with only a change in the input data.

The ‘bursting’ phenomenon in a turbulent boundary layer

Abstract: Using a hot wire in a turbulent boundary layer in air, an experimental study has been made of the frequent periods of activity (to be called ‘bursts’) noticed in a turbulent signal that has been passed through a narrow band-pass filter. Although definitive identification of bursts presents difficulties, it is found that a reasonable characteristic value for the mean interval between such bursts is consistent, at the same Reynolds number, with the mean burst periods measured by Kline et al. (1967), using hydrogen-bubble techniques in water. However, data over the wider Reynolds number range covered here show that, even in the wall or inner layer, the mean burst period scales with outer rather than inner variables; and that the intervals are distributed according to the log normal law. It is suggested that these ‘bursts’ are to be identified with the ‘spottiness’ of Landau & Kolmogorov, and the high-frequency intermittency observed by Batchelor & Townsend. It is also concluded that the dynamics of the energy balance in a turbulent boundary layer can be understood only on the basis of a coupling between the inner and outer layers.

Non-linear resonant instability in boundary layers

Abstract: An investigation is made of resonant triads of Tollmien-Schlichting waves in an unstable boundary layer. The triads considered are those comprising a two-dimensional wave and two oblique waves propagating at equal and opposite angles to the flow direction and such that all three waves have the same phase velocity in the downstream direction. For such a resonant triad remarkably powerful wave interations take place, which may cause a continuous and rapid transfer of energy from the primary shear flow to the disturbance. It appears that the oblique waves can grow particularly rapidly and it is suggested that such preferential growth may be responsible for the rapid development of three-dimensionality in unstable boundary layers. The non-linear energy transfer primarily takes place in the vicinity of the critical layer where the downstream propagation velocity of the waves equals the velocity of the primary flow.The theoretical analysis is initially carried out for a general primary velocity profile; then, in order to demonstrate the essential features of the results, precise interaction equations are derived for a particular profile consisting of a layer of constant shear bounded by a uniform flow. Some exact solutions of the general interaction equations are presented, one of which has the property that the wave amplitudes become indefinitely large at a finite time. The possible relevance of the present theoretical model to the experiments of Klebanoff, Tidstrom & Sargent (1962) is examined.

Numerical solution of the interaction of a shock wave with a laminar boundary layer

Abstract: Shock wave interaction with laminar boundary layer on flat plate using modified Lax-Wendroff difference technique

The response of a turbulent boundary layer to a step change in surface roughness Part 1. Smooth to rough

Abstract: An experimental study of the structure of the internal layer which grows down-stream from a rough-to-smooth surface change shows it to be essentially different from that studied by Antonia & Luxton (1971 b) for the case of a smooth-to-rough perturbation. The rate of growth of the internal layer is less than that for the smooth-to-rough step and it appears that the more intense initial rough-wall flow dictates the rate of diffusion of the disturbance for a considerable distance. Inside the internal layer the mixing length I is increased relative to the equilibrium distribution I = KY. A turbulent energy budget shows that the advection is comparable with the production or dissipation, whilst there seems to be some diffusion of energy into the internal-layer region close to the wall. The boundary layer, as a whole, recovers much more slowly following a rough-to-smooth change than following a smooth-to-rough change, and at the last measuring station (16 boundary-layer thicknesses from the start of the smooth surface) the distributions of mean velocity and Reynolds shear stress are far from self-preserving.

Local non- similarity thermal boundary- layer solutions

Abstract: A solution method is described and applied for treating non-similar thermal boundary layers. The solutions are locally autonomous (that is, independent of information from other streamwise locations) and are found by solving quasi-ordinary differential equations of the similarity type. All non-similar terms appearing in the conservation equations are retained without approximation, and only in derived subsidiary equations are terms selectively neglected. The accuracy of the results can be appraised from comparisons internal to the method itself. Thermal boundary-layer non-similarity arising both from velocity-field, non-similarity and from streamwise variations of surface temperature are analyzed. Numerical results for the surface heat transfer and for the boundary-layer temperature distribution are presented for various physical situations.

General Analysis of Longitudinal Dispersion in Nonuniform Flow

Abstract: An analytical method is proposed by which the effects of flow nonuniformity and variable dispersion coefficients can be evaluated for problems involving longitudinal dispersion in porous media. A boundary layer approximation is used to develop general solutions of the one-dimensional convective-dispersion equation for steady flow. Several examples are considered by using the analytical method, and the general effect of flow nonuniformity on dispersion is discussed. Comparisons of the analytical solution with numerical solutions of the exact equation indicate that the method will yield accurate results in many applications.

Oxidation/Vaporization Kinetics of Cr2O3

Abstract: The weight loss of Cr2O3 in oxidizing environments (Po2= 1 to 10−3 atm) at 1200°C was measured. Both hot-pressed and sintered Cr2O3 pellets were investigated in O2/Ar gas mixtures, and the dependence of the weight loss on the O2 partial pressure, the gas flow rate, and the total pressure was determined independently. The experimentally determined O2 partial pressure dependence (rate ∝ PO23/4) corresponds to that expected for the reaction Cr2O3(s)+3/2O2⇌2CrO3(g). The flow rate and total pressure dependencies show that mass transport through a gaseous boundary layer is the rate-controlling step in the oxidation/vaporization of Cr2O3. Evaporation coefficients for the loss of CrO3(g) under the experimental conditions were <0.01.

Survey of viscous interactions associated with high Mach number flight

Abstract: T most severe problems of atmospheric flight at high Mach numbers are associated with viscous-inviscid interactions. Cruise vehicles for Mach numbers above four and lifting re-entry vehicles have highly complex three-dimensional configurations in which exist many regions of high compression that can cause boundary layers to separate. Although separation can result in loss of control effectiveness or flow degradation in an engine inlet, flow reattachment gives rise to heat rates that can far exceed those for an attached boundary layer. A further, and possibly far more severe viscous interaction problem is the impingement of shock waves generated by the forebody and other external components of a vehicle on aft sections resulting in local heat rates that may be many times larger than stagnation point values. Peak heating conditions may be laminar for lifting re-entry configurations, though our knowledge of boundary layertransition is far from adequate so that transitional and turbulent flows cannot be ruled out. However, Reynolds num, bers of potential high Mach number cruise vehicles are high— 10 to 10—so that viscous interactions will be predominately associated with turbulent boundary layers and their attendant higher heat rates. The high local heat rates resulting from viscous interactions cause "hot spots" that could lead to catastrophic failure. Vivid examples of damage resulting from viscous interactions are given in Figs. 1 and 2. A ventral pylon on the X-15 airplane, shown in Fig. 1, caused high^local heating of the fuselage around its root, and developed large holes near its tip due to the impingement of the shock wave from a dummy ramjet it supported, during a flight at Mach 6.7 in 1967. A study of the flowfield of the pylon-mounted dummy ramjet configuration is reported in Ref. 1. Figure 2 shows considerable damage due to interaction heating to the underside of a sled and its supporting slipper as a result of a run at 7000 fps on the 7-mile test track at Holloman Air Force Base. Unlike stagnation-point heating where the location is obvious, the problem with complex configurations is to determine "where" high heat rates are likely to occur, as well as their magnitude. It is the purpose of this paper to identify some potentially critical areas of viscous interactions associated with high Mach number vehicles and briefly review our state of knowledge in these areas with emphasis on the basic flow phenomena.

Extension of Emmons' spot theory to flows on blunt bodies

Abstract: The transition region is considered to be characterized by the intermittent appearance of turbulent spots, which grow as they move downstream until they finally merge into one another to form the turbulent boundary layer. The intermittency factor for arbitrary axisymmetric body with zero angle of attack has been derived in an expression which can be reduced to the form of universal intermittency distribution of Dhawan and Narasimha in the case of straight tube or flat plate. A key factor to control flow conditions in the transition zone appears to be the spot formation rate, which has been deduced from the available data of the extent of transition zone. It was found that the spot formation rate depends not only on the transition Reynolds number but also on the Mach number. A comparison of the deduced spot formation rate with the neutral stability curves indicated that the neutral stability curves can be used as a guide to relate the spot formation rate to the transitional Reynolds number. Calculations of the transitional heat-transfer rate on a sphere in supersonic flow agree well with the experimental results.

Calculation of boundary-layer development using the turbulent energy equation: compressible flow on adiabatic walls

Abstract: The basic method described by Bradshaw, Ferriss & Atwell (1967) is extended to compressible flow in two-dimensional boundary layers in arbitrary pressure gradient (excluding shock waves and expansion fans) by invoking Morkovin's hypothesis (Favre 1964) that the turbulence structure is unaffected by compressibility Using the same empirical functions as in incompressible flow, skin friction in zero pressure gradient is predicted to within 3% of Spalding & Chi's (1964) correlation for free-stream Mach numbers less than 5 Comparisons with experiments in pressure gradient are restricted by the lack of data, but, since Morkovin's hypothesis does not depend on pressure gradient, methods which use it (of which the present method seems to be the first) can be checked fairly adequately by comparisons with data in zero pressure gradientNo ‘compressibility transformations’ are needed, although the Crocco relation is used, provisionally, for the temperature: since the calculations take only about 20% longer than in incompressible flow, Morkovin's hypothesis does as much as any transformation could do It is pointed out that, in supersonic flow, surface curvature which is large enough to induce a significant longitudinal pressure gradient is also large enough to have a very significant effect on the turbulence structure

Spatial structure in the viscous sublayer

Abstract: An experimental investigation was performed to study the spatial coherence of structures in the sublayer of a turbulent boundary layer observed previously by flow visualization. The present work verifies these observations in an Eulerian reference frame and develops a statistical description of the phenomenon. The technique involves simultaneous digital sampling of an array of constant temperature hot-wire anemometers arranged to extract information about a spanwise variation in flow quantities. The quantitative description agrees with dimensionless measures of the structure scales previously published.

Accurate numerical methods for boundary layer flows I. Two dimensional laminar flows

Abstract: A very simple and accurate numerical scheme which is applicable t o quite general boundary layer flow problems has been devised. It has been tested extensively on laminar flows, turbulent flows (using the eddy viscosity and eddy conductivity formulations), wake flows and many other such problems. In the brief space alloted to us here we shall illustrate the method by showing its application in some detail to nonsimilar plane laminar incompressible boundary layers and in particular to the well known case of Howarth's flow [3] .

Calculation of Compressible Turbulent Boundary Layers with Heat and Mass Transfer

Abstract: In this paper we present a general method for calculating turbulent boundary layers in twodimensional flows and investigate its accuracy for compressible flows with heat and mass transfer The method is based on the ideas of eddy transport coefficients and the numerical solution of the governing equations in differential form The experimental data considered cover a Mach number range of 0 to 67 and include flows with and without pressure gradients The results indicate good agreement at high Reynolds numbers At low Reynolds numbers the agreement is not as good, and further work needs to be done in such cases

The sea surface temperature deviation and the heat flow at the sea-air interface

Abstract: The deviation of the sea surface temperature from the water temperature below is calculated as a function of the heat flow through the air-sea interface, using wind tunnel determinations of the effective thermal diffusivity in a boundary layer. The influence ofQ, shortwave radiation, andH, latent and sensible heat transfer plus effective back radiation, and U, wind speed, can be described by:T0 −Tw =C1 ·H/U +C2 ·Q/U. The calculated coefficients vary slightly with reference depth, Tables II and III. They are in good agreement with independent observations.

Boundary layer resistance and temperature distribution on still and flapping leaves: I. Theory and laboratory experiments.

Abstract: If the evaporation is uniform on a flat exposed leaf, forced convection will also be nearly uniform, and the leaf temperature will vary with the square root of the distance from the leading edge. Then the resistance expressed in terms of the proper, i.e., average, temperature has the same value as the resistance of a leaf at uniform temperature. Compared to a steady laminar flow, the turbulence of a realistic wind decreases the resistance by a constant factor of about 2.5. The same constant factor was observed whether the leaf was flapping or not, when the wind velocity was not too low.

Mean Period of the Turbulent Production Mechanism in a Boundary Layer

Abstract: Based on experimentally observed scaling laws, the interaction between the motion in the sublayer with that of the wakelike outer flow is described in terms of a limit cycle.

Flow and pressure drop in systems of repeatedly branching tubes

Abstract: The airways of the lung form a rapidly diverging system of branched tubes, and any discussion of their mechanics requires an understanding of the effects of the bifurcations on the flow downstream of them. Experiments have been carried out in models containing up to two generations of symmetrical junctions with fixed branching angle and diameter ratio, typical of the human lung. Flow visualization studies and velocity measurements in the daughter tubes of the first junction verified that secondary motions are set up, with peak axial velocities just outside the boundary layer on the inner wall of the junction, and that they decay slowly downstream. Axial velocity profiles were measured downstream of all junctions at a range of Reynolds numbers for which the flow was laminar.In each case these velocity profiles were used to estimate the viscous dissipation in the daughter tubes, so that the mean pressure drop associated with each junction and its daughter tubes could be inferred. The dependence of the dissipation on the dimensional variables is expected to be the same as in the early part of a simple entrance region, because most of the dissipation will occur in the boundary layers. This is supported by the experimental results, and the ratio Z of the dissipation in a tube downstream of a bifurcation to the dissipation which would exist in the same tube if Poiseuille flow were present is given by \[ Z = (C/4\surd{2})(Re\,d/L)^{\frac{1}{2}}, \] where L and d are the length and diameter of the tube, Re is the Reynolds number in it, and the constant C (equal to one for simple entry flow) is equal to 1·85 (the average value from our experiments). In general, C is expected to depend on the branching angles and diameter ratios of the junctions used. No experiments were performed in which the flow was turbulent, but it is argued that turbulence will not greatly affect the above results at Reynolds numbers less than and of the order of 10000. Many more experiments are required to consolidate this approach, but predictions based upon it agree well with the limited number of physiological experiments available.

The response of a tropical cyclone model to variations in boundary layer parameters, initial conditions, lateral boundary conditions, and domain size

Abstract: Tropical cyclone model experiments are summarized in which the drag coefficient and the analogous exchange coefficients for sensible and latent heat are varied. During the early portions of the immature stage, the response of the model storm follows linear theory and growth is more rapid with larger drag coefficients. However, the ultimate intensity reached by model storms varies inversely with the drag coefficient. The experiments indicate that air-sea exchanges of latent heat are crucial for the development and maintenance of the model storm. The air-sea exchange of sensible heat appears to be far less important. Experiments conducted with open lateral boundary conditions revealed that the structure and intensity of the mature stage of the model cyclone is relatively insensitive to the initial perturbation and to the size of the computational domain. The time required to reach the mature stage is, however, quite sensitive to these influences. Comparisons between experiments with open and mechan...

Boundary Layer Induced by a Potential Vortex

Abstract: A numerical computation of the laminar boundary layer on a fixed circular disk of radius a whose axis is concentric with that of a vortex having circulation Γ is described. The computations were started at the edge of the disk and continued inward toward the axis until the properties of the terminal flow became evident. A two‐layer asymptotic expansion was formulated for the solution of the boundary‐layer equations near the axis, and the terminal‐flow properties revealed by the analysis are shown to be in excellent agreement with the numerical results. The structure of the terminal boundary layer consists of an inner layer next to the surface with thickness O[(ν/Γ)1/2r] in which the flow is primarily radial, and an outer layer with thickness O[(ν/Γ)1/2a] of predominantly inviscid nature in which the flow recovers to the external potential vortex. The mass flux in the outer layer does not vanish as r→0, indicating that the boundary layer must erupt from the surface at r=0in the manner envisioned by Moore.